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Hard Gluon Damping in Hot QCD: Implications and Non-Perturbative Effects

This paper investigates the impact of hard gluon damping in hot Quantum Chromodynamics (QCD), examining both one-particle and many-particle properties. Key areas explored include thermodynamic potentials, transport coefficients, and non-zero width effects on thermodynamic consistency. The study shows the relevance of self-consistent resummation methods for accurately predicting quasiparticle properties, especially under strong coupling scenarios. The findings highlight the significance of damping rates and spectral functions, particularly near the QCD phase transition, providing valuable insights into QCD thermodynamics.

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Hard Gluon Damping in Hot QCD: Implications and Non-Perturbative Effects

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  1. Hard Gluon damping in hot QCD hep-ph/0403225André Peshier *Institut for Theoretical Physics, Giessen University QCD thermodynamics Effects due to non-zero width Implications * supported by BMBF

  2. 1-particle & many-particle properties • bulk properties (pressure, entropy, density …) • transport properties (viscosities, conductivities) • … entropy dispersion relation damping rate = width • weak coupling QCD, • strong coupling QCD, near • … large width ?? • lattice QCD: ??? self-consistent resummation:non-trivial • gauge invariance • non-perturbative renormalization • thermal masses • expectation quasiparticles • : (HTL) resummation required already at leading order! IR divergence; generic sensitivity to non-perturbative sector [Pisarski, …] A. Peshier, Hard gluon damping in hot QCD

  3. lattice QCD phase transition at QCD (here:quenched) thermodynamics • perturbation theory „diverges“ for large coupling [Arnold et al.] [Boyd et al., CPPACS] A. Peshier, Hard gluon damping in hot QCD

  4. ‘partition function’ asymptotic series cut in complex  plane ~# diagrams i) truncate at low order ii) resum Divergent series, toy model + + … A. Peshier, Hard gluon damping in hot QCD

  5. Resummation in theory • propagator • thermodynamic potential [Luttinger, Ward, …] A. Peshier, Hard gluon damping in hot QCD

  6. -derivable (sc) approximations • ‘large coupling resum leading-loop order’ NB: resummation necessary for thermodynamic consistency • cf. screend perturbation theory [Karsch et al.] truncate & calc. selfconst’ly non-perturbative renormalization! A. Peshier, Hard gluon damping in hot QCD

  7. phenomenological QP models interacting gluons massive QP [Peshier et al.] Interlude: QCD quasiparticle models based on appropriate approximations of propagators • HTL QP models • HTL entropy:[Blaizot et al.] • HTL pressure: [Peshier] • HTL pT:[Braaten et al.] A. Peshier, Hard gluon damping in hot QCD

  8. Relevance of width large qp mass  • near Tc: small entropy • entropy (~ population of phase space)  large coupling  large width?? affected by mass & width A. Peshier, Hard gluon damping in hot QCD

  9. Dynamical quasiparticle entropy • Luttinger-Ward formalism • consider entropy • leading-loop resummation for large coupling contribs. from graphs with more than 2 vertices quasiparticles with dispersion rel. effect of finite width A. Peshier, Hard gluon damping in hot QCD

  10. Width increases entropy, i) properties of propagator & spectral function retarded propagator: A. Peshier, Hard gluon damping in hot QCD

  11. Width increases entropy, ii)two typical cases for propagator `regular´ `singular´ common: `dispersion relation´ determined by real part of self-energy A. Peshier, Hard gluon damping in hot QCD

  12. Width increases entropy, iii)integrand of `rather symmetric´ (more rigorously: hep-ph/0403225) exp. decreasing under rather general assumptions: A. Peshier, Hard gluon damping in hot QCD

  13. Lorentz spectral function introduce width parameterize `dispersion relation´ by mass A. Peshier, Hard gluon damping in hot QCD

  14. Entropy for Lorentz spectral function cf. phenomeno- logical QP models in QCD: can be large near ? A. Peshier, Hard gluon damping in hot QCD

  15. Momentum dependence of and • quantify: bulk properties are determined by hard momenta negligible sensitivity on small A. Peshier, Hard gluon damping in hot QCD

  16. Sensitivity on shape of spectral function? example: `quartic´ spectral function NB: chose same dispersion relation to compare to Lorentzian A. Peshier, Hard gluon damping in hot QCD

  17. Spectral function in Fourier space • model peaked at damping (need not be exponential) (from sum rule) typical attenuation time `forward´ Fourier transform A. Peshier, Hard gluon damping in hot QCD

  18. Non-exponential time behavior • damping models with their Fourier transform A. Peshier, Hard gluon damping in hot QCD

  19. Polynomial models expectation: sensitivity on long-time behavior, insensitive to short-time behavior width has strong effect on entropy except for singular spectral functions A. Peshier, Hard gluon damping in hot QCD

  20. QCD • approximately self-consistent scheme • entropy dominated by transverse modes (longitudinal excitations: collective, give small contribution to HTL entropy) gauge invar.! parameterized by and (gauge inv.) A. Peshier, Hard gluon damping in hot QCD

  21. QCD : `quasiparticles´ with width • a phenomenological parametrization NB: is not just a 3rd fit parameter, functional form fixed! • assumptions • soft gluons: HTL, • hard gluons: • magn. mass • IR regulator, pole struct. [Pisarski, …] A. Peshier, Hard gluon damping in hot QCD

  22. QCD : quasiparticles? • small for , • result robust (cf. hep-ph/…) QP! • fulfilled … width ~ mass A. Peshier, Hard gluon damping in hot QCD

  23. Implications • estimate magnetic mass: [Nakamura et al.] A. Peshier, Hard gluon damping in hot QCD

  24. Implications • empirical observation for Debye mass: [Nakamura et al.] A. Peshier, Hard gluon damping in hot QCD

  25. Implications • radiative energy loss~missing jet quenching at SPS • parton in (quark-) gluon plasma of extent L • several independent scatterings ( ): LPM regime • for [Baier et al.] again at : characteristic changes in observables A. Peshier, Hard gluon damping in hot QCD

  26. Resumé • width has significant effect on thermodyn. bulk properties (unless for exotic spectral functions) • for QCD at : broad exciations for : heavy narrow modes (quasiparticles) • charact. (universal?) temp. could be observable A. Peshier, Hard gluon damping in hot QCD

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